Fix: Guard with lock when accessing background counters.

This reverts commit d5f3e225.

CQ_INCLUDE_TRYBOTS=luci.v8.try:v8_linux64_tsan_rel

Change-Id: I4e00f41ce6a2fac86d4e90c70e57c7a333442a97
Reviewed-on: https://chromium-review.googlesource.com/c/1301503Reviewed-by: Ulan Degenbaev <ulan@chromium.org>
Commit-Queue: Michael Lippautz <mlippautz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#57027}